Cut-off and Escape Behaviors for Birth and Death Chains on Trees
Probability
2011-02-11 v3 Mathematical Physics
math.MP
Abstract
We consider families of discrete time birth and death chains on trees, and show that in presence of a drift towards the root of the tree, the chains exhibit cut-off behavior along the drift and escape behavior in the opposite direction.
Cite
@article{arxiv.1006.4324,
title = {Cut-off and Escape Behaviors for Birth and Death Chains on Trees},
author = {Olivier Bertoncini},
journal= {arXiv preprint arXiv:1006.4324},
year = {2011}
}
Comments
22 pages, 1 figure. This new version, written after referee's suggestions, is shorter and features a more clear presentation of the results. The previous proofs of Section 3, based on difference equations method, are now given in appendix